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A round-robin tournament involving n plays is modeled with digraph D where, for every two distinct...

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Advance Math

A round-robin tournament involving n plays is modeled withdigraph D where, for every two distinct vertices (players) u and v,either (u,v) is an edge (player u defeats player v) or (v,u) is anedge (player v defeats play u). Prove that if D is acyclic, i.e.,no directed cycles, then there always exists a player who hasdefeated everyone (out-degree is n – 1) and a player who has lostto everyone (in-degree is n – 1).

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